Problem: Ishaan is 5 times as old as Ben. Four years ago, Ishaan was 7 times as old as Ben. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of Ishaan and Ben. Let Ishaan's current age be $i$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $i = 5b$ Four years ago, Ishaan was $i - 4$ years old, and Ben was $b - 4$ years old. The information in the second sentence can be expressed in the following equation: $i - 4 = 7(b - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = i / 5$ . Substituting this into our second equation, we get: $i - 4 = 7($ $(i / 5)$ $- 4)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 4 = \dfrac{7}{5} i - 28$ Solving for $i$ , we get: $\dfrac{2}{5} i = 24$ $i = \dfrac{5}{2} \cdot 24 = 60$.